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28 July, 01:52

1. For the Summer R&B/Soul Festival, there is one price for students, one for adults, and another for senior citizens. The Jackson family bought 3 student tickets and 2 adult tickets for $104. The Williams family bought 5 student tickets, 1 adult ticket, and 2 senior citizen tickets for $155. The Mullins family bought 2 of each for $126. a. Write a system of equations that can be used to find the cost of each ticket. b. Solve the system by elimination to find the cost of each ticket.

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  1. 28 July, 02:11
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    Step-by-step explanation:

    Let's call student tickets s, adult tickets a and senior tickets c. The equations for each family are as follows:

    Jackson: 3s + 2a = 104

    Williams: 5s + 1a + 2c = 155

    Mullins: 2s + 2a + 2c = 126

    To get started, let's solve the Jackson family equation for a:

    2a = 104 - 3s so

    a = 52 - 1.5s

    Now we can use that a value in the Williams equation:

    5s + 1 (52 - 1.5s) + 2c = 155 and

    5s + 52 - 1.5s + 2c = 155 and

    3.5s + 2c = 103

    We can also use that a value in the Mullins equation:

    2s + 2 (52 - 1.5s) + 2c = 126 and

    2s + 104 - 3s + 2c = 126 so

    -1s + 2c = 22

    Solve the system that is in bold print now by multiplying the Mullins equation through by - 1 to get a new system that looks like this:

    3.5s + 2c = 103

    1s - 2c = - 22

    The c's eliminate each other leaving us with only s's:

    4.5s = 81 so

    s = 18

    The cost of a student ticket is $18. Now use that $18 in place of s in the first bold equation above:

    3.5 (18) + 2c = 103 and

    63 + 2c = 103 and

    2c = 40 so

    c = 20

    The cost of a senor ticket is $20. Now use both of those values in the Williams equation at the beginning to solve for a:

    5 (18) + 1a + 2 (20) = 155 and

    90 + 1a + 40 = 155 and

    1a = 25

    The cost of an adult ticket is $25
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